English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

(4, 5), (7, 6), (4, 3), (1, 2)

Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).

Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.

If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).

If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?

If a≠b≠0, prove that the points (a, a²), (b, b²) (0, 0) will not be collinear.

If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y

What is the HCF of the smallest prime number and the smallest composite number?

Find the distance of a point P(x, y) from the origin.

Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.

A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

Find the distance between the following pair of points:

(-6, 7) and (-1, -5)

Find the distance between the following pair of points:

 (a+b, b+c) and (a-b, c-b)

Find the distance between the following pair of points:

(asinα, −bcosα) and (−acos α, bsin α)

Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`

If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.

Find the values of x, y if the distances of the point (x, y) from (-3, 0)  as well as from (3, 0) are 4.

The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.